Abstract

Let n be the symmetric group of degree n, and let F be a field
of characteristic p 6= 2. Suppose that is a partition of n+1, that and are
partitions of n that can be obtained by removing a node of the same residue
from , and that dominates . Let S and S be the Specht modules, defined
over F, corresponding to , respectively . We give a very simple description
of a non-zero homomorphism : S → S and present a combinatorial proof
of the fact that dimHomFn(S, S) = 1. As an application, we describe
completely the structure of the ring EndFn(S ↓n ). Our methods furnish
a lower bound for the Jantzen submodule of S that contains the image of .